(Milton). 2. Pure of manners; honest; good.

INCORRUPTIBILITY. s. (incorruptibi. lité, French.) Insusceptibility of corruption; incapacity of decay (Hakewill).

INCORRUPTIBLE. a. (incorruptible, Fr.) Not capable of corruption; not admitting decay (Wake).

INCORRUPTION. s. (incorruption, Fr.) Incapacity of corruption (Cor.).

INCORRUPTNESS. 8.(from incorrupt.) 1. Purity of manners; honesty; integrity (Woodward). 2. Freedom from decay or de. generation.

To INCRA'SSATE. v. a. (in and crassus, Lat.) To thicken; the contrary to attenuate (Brown. Newton).

INCRASSATED peduncle. In botany, a peduncle thickening or becoming thicker towards the flower; as in Cotula, Tragopogon, and most cernuous flowers. Opposed to attenuate. It is applied also to the scape. INCRASSA'TION. 8. (from incrassute.) 1. The aet of thickening. 2. The state of growing thick (Brown).

INCRA'SSATIVE. a. (from incrassate.) Having the quality of thickening (Harvey). To ÎNCREASE. v. n. (in and cresco, Lat.) 1. To grow more or greater; to advance in quantity or value (Prior). 2. To be fertile (Hale).

To INCREASE. v. a. To make more or greater (Temple).

INCREASE. 8. (from the verb.) 1. Angmentation; the state of growing more or greater (Pope). 2. Increment; that which is added to the original stock (Leviticus). 3. Produce (Denham). 4.Generation (Shaks.). 5. Progeny (Pope). 6. The state of waxing (Bacon).

INCREASER. s. (from increase.) He

who increases.

INCREATED. a. Not created (Cheyne). INCREDIBILITY. 8. (incredibilité, Fr.) The quality of surpassing belief (Dryden). INCREDIBLE. a. (increuibiis, Lat.) Surpassing belief; not to be credited (Raleigh).

INCREDIBLENESS. 8. (from incredible.) Quality of being not credible.

INCREDIBLY. ad (from incredible.) In a manner not to be believed.

INCREDULITY. s. (incredulité, French.) Quality of not believing; hardness of belief (Raleigh).

INCREDULOUS. a. (incredule, Fr. incredulous, Latin.) Hard of belief; refusing credit (Bacon).

INCREDULOUSNESS. 8. (from incredu lous) Hardness of belief; incredulity. INCRE/MABLE. a. (in and cremo, Latin). Not consumable by fire (Brown).

INCREMENT. s. (incrementum, Latin). 1. Act of growing greater (Brown). 2. I. crease; matter added (Woodward). 2. Produce (Philips).

INCREMENT, in mathematics, the small

increase of a variable quantity. Newton, in his Treatise on Fluxions, calls these by the name moments, and observes, that they are proportional to the velocity or rate of increase of the variable quantities in an indefinitely small time.

I'NCREMENTS, METHOD OF, a branch of analytics, in which a calculus is founded on the properties of the successive values of variable quantities, and their differences or increments.

This method was invented by Dr. Brook Taylor, who published a treatise upon it in 1715, and who farther explained it in the Philosophical Transactions. It is nearly allied to the method of fluxions, and indeed arises out of it: in many respects it is of the same nature as the differential method, but is more general. It is very useful in diffe rent mathematical pursuits; but more particularly in the summation of series, where it is of very ready and extensive applica tion.

In this method any variable quantity is called an integral. The magnitude by which it is increased at one step is called the increment. Thus, 1+2+3 . +m=m.

mand the magnitude by which it in

creases at one step is m+1, which is called the increment of the integral m.

m+1

duct of quantities in arithmetical progres

....

sion, as m. m+r. m+2r. m+3r. mta—1.r, where r is constant, and m is increased at every step by r, the increment of

this integral is nr×m+r. m+2r. m+3r.

..m+n-1.r. And since an invariable quantity C has no increment, if such quantity be added to, or taken from, the above quantities, the increment of the whole will remain the same. Hence, if the increment of an integral be represented by n r× m+r. m+2r. m+3 r......... .m + n−1. r, the integral is m. m+r. m+2r. m+3r. ........m+n−1. r + C; where the invariable quantity C must be determined by the nature of the question.

To find, therefore, the integral of any increment, let the increment be reduced to the products of arithmetical progressionals, whose common difference is the quantity by which the variable magnitude is increased at every step, and the integral of each increment will be found by multiplying it by the preceding term in the progression, and dividing it by the number of terms thus increased, and by the common difference. This result is to be increased or lessened by the constant quantity C: thus, when x, the integral obtained by the rule, is a, suppose the true integral is known to be b; then since +C is in all cases the integral, and a+C-b, or C-b-a, therefore the correct integral is x+b—a.

Though in general it is convenient to reduce an increment to the product of arithmetrical progressionals, in order to obtain its integral; yet, if a quantity of any other form can be found, whose increment coincides with that proposed, this quantity, when properly corrected, is the integral. Er. Find the sum of n terms of the series 5+6+7, &c. Let A n + Bn2 +Сn3+, &c. be the sum required; its increment is A. n+1+B⋅n +1 2+C.n+1, 3, &c.—A n-Bn2 Ca, &c.; and the increment of the sum is also +5; therefore A+2 B n+B+3 C 2 +3 C n+C+ &c.=n+5; and by equating the co-efficients, C=0; 2 B=1, or B=1; A+B=5, or A=£; hence, the sum required which needs no correction.

is

2

Those who wish to prosecute this subject farther, are referred to Wood's Algebra, Emerson's Increments, Hutton's Dict. art. Increments, Simpson's Exercises, Taylor's Method. Increment. and Waring's Medita. Analyt. lib. 2.

TVNCREPATE. v. a. (increpɔ, Latin) To chide; to reprehend. VOL. VI.

additional coat adhering to the internal matter (Pope. Cheyne).

INCRUSTĂ TÍON. s. (incrustation, Fr.) An adherent covering; something superinduced (Addison).

To INCUBATE. v. n. (incubo, Latin.) To sit upon eggs.

INCUBATION, in ornithology, that part of the general process of ovation which consists in the sitting of the hen upon her eggs, in order to hatch them. See OVATION.

This

I'NCUBUS, (Incubus, i, m. from incubo. to lie upon, because the patient fancies that something lies upon his chest.) See NIGHTMARE, and ONEIRODYNIA GRAVENS. disease was denominated by the Greek physicians Ephialtes, a term still continued in Sauvages and some other nosologists.

To ÎNCULCATE. v. a. (inculco, Lat.) To impress by frequent admonitions (Broome). INCULCATION. s. (from inculcate.) The act of impressing by frequent admonition. INCULPABLE. a. (in and culpabilis, Lat.) Unblamable; not reprehensible (South). IŃCU'LPABLY. ud. (in and culpabilis, Lat.) Unblamably; without blame (South). INCULT. a (inculte, Fr. incultus, Latin.) Uncultivated; untilled (Thomson).

INCUMBENCY. s. (from incumbent.) 1. The act of lying upon another. 2. The state of keeping a benefice (Swift).

INCUMBENT. a. (incumbens, Latin.) 1. Resting upon; lying upon (Boyle). 2. Imposed as a duty (Sprat).

INCUMBENT. Incumbens. In botany, leaning upon, or resting against. Applied to the stamens in the class diadelphia; to anthers, which rest upon the filament: opposed to upright, erecta; to the divisions of leaves which lie one over another.

INCUMBENT, a clerk, or minister, who is resident on his benefice: he is called incumbent, because he does, or at least ought to bend his whole study to discharge the cure of his `church.

To INCUMBER. v. a. (encombrer, Fr.) To embarrass (Dryden).

To INCUR. v. a. (incurro, Latin.) 1. To become liable to a punishment or reprehension (Hayward). 2. To occur; to press on the senses (South).

INCURABILITY, s. (incurabilité, Fr.) Impossibility of cure; utter insusceptibility of remedy (Harvey).

INCURABLE. a. (incurable, French.) Not admitting remedy; not to be removed by medicine, irremediable; hopeless (Sw.),

INCURABLENESS. s. (from incurble.) State of not admitting any cure.

INCURABLY. ad. (from incurable.) Without remedy (Locke).

INCU'RIOUS. a. (in and curious). Negli. gent; inattentive (Denham).

U

INCURSION. 8. (from incurro, Latin.) 1. Attack; mischievous occurrence (South). 2. (Incursion, French.) Invasion without conquest; inroad; ravage (Bacon). To INCURVATE. v. a. (incurvo, Latin.) To bend; to crook (Cheyne),

INCU'RVATE STEM. In botany, an incurved stem. Introrsum nutans. Delin. Pl. bowed or curved inwards; incurvate leaf; dum sursum arcuatur versus caulem; bowed or curved upwards towards the stem. Made to be sy nonymous with inflexum in Philos. Bot.; aculeus incurvus; introrsum flexus; a pric. kle, bowed or bent inwards. The terms for angular and curvi-linear bendings ought to be distinct; bent should be applied to the first, and bowed or curved to the second.

INCURVA/TION. s. (from incurvate.) 1. The act of bending or making crooked. 2. State of being bent; curvity; crookedness (Glanville). 3. Flexion of the body in token of reverence (Stillingfleet).

INCU'RVITY. 8. (from incurvus, Latin.) Crookedness; the state of bending inward (Brown).

INCUS, (Incus, udis, f. a smith's anvil, from incudo, to smite upon; so named from its likeness in shape to an anvil.) The largest and strongest of the bones of the ear in the tympanum. It is divided into a body and two crura. Its body is situated anteriorly, is rather broad than thick, and has two eminences and two depressions, both covered with cartilage, and intended for the reception of the head of the malleus. Its shorter crus extends no farther than the cells of the mastoid apophysis. Its longer crus, together with the manubrium of the malleus, to which it is connected by a ligament, is of the same extent as the shorter, but its extremity is curved inwards to receive the os orbiculare, by the intervention of which it is united with the stapes.

To INDAGATE. v. a. (indago, Lat.) To search; to beat out.

INDAGA'TION. 8. (from (indagate.) Search inquiry; examination (Boyle).

INDAGATOR. s. (indagator, Latin.) A searcher; an inquirer; an examiner (Boyle). To INDART. v. a. (in and dart.) To dart in; to strike in (Shak.).

To INDEBT. v. a. 1. To put in debt. 2. To oblige to put under obligation (Milton). INDEBTED. participial a. (in and debt.) Obliged by something received; bound to restitution; having incurred a debt (Hook).

INDE/CENCY. s. (indecence, Fr.) Any thing unbecoming; any thing contrary to good manners; something wrong, but scarce criminal (Locke).

INDE CENT. a. (indecent, Fr.) Unbecoming; unfit for the eyes or ears (South). INDECENTLY. ad. Without decency; in a manner contrary to decency.

INDECIDUOUS. a. (in and deciduous.) Not falling; not shed; not liable to a yearly fall of the leaf; evergreen (Brown).

INDECLINABLE. a.

(indeclinabilis, Lat.) Not varied by terminations (Arbuthnot), INDECO'ROUS. a. (indecorus, Latin. Indecent; unbecoming (Norris). INDECO'RUM. s. (Latin.) Indecency; something unbecoming (Young).

INDEED. ad. (in and deed.) 1. In reality; in truth; in verity (Sidney). 2. Above common rate (Davies). 3. This is to be granted that; he is wise indeed, but he is not happy (Wake). 4. It is used as a slight assertion or recapitulation in a sense hardly perceptible or explicable: I said I thought it a confederacy, though indeed I had no rea son so to think (Bacon). 5. It is used to note concessions in comparisons; he is a greater man indeed, but not a better (Bacon). INDEFATIGABLE. a. (indefatigabilis, Latin.) Unwearied; not tired; not exhausted by labour (South).

INDEFATIGABLY. ad. (from indefatigable.) Without weariness (Dryden).

INDEFECTIBILITY. 8. (from indefecti ble.) The quality of suffering no decay; of being subject to no defect.

INDEFECTIBLE. a. (in and defectus, Latin.) Unfailing; not liable to defect or decay.

INDEFEUSABLE. a. (indefaisible, Fr.) Not to be cut off; not to be vacated; irrevocable (Decay of Piety).

INDEFENSIBLE. a.(in and defensus, Latin.) What cannot be defended or maintained (Sandys).

INDEFINITE. a. (indefinitus, Latin.) 1. Not determined; not limited; not settled (Bacon). 2. Large beyond the comprehension of man, though not absolutely without limits (Spectator).

INDEFINITE is also used in the schools to signify a thing that has but one extreme; for instance, a line drawn from any point and extended infinitely.

INDEFINITE, in grammar, is understood of nouns, pronouns, verbs, participles, articles, &c. which are left in an uncertain indeterminate sense, and not fixed to any particular time, thing, or other circuni

stance.

INDEFINITELY. ad. 1. Without any settled or determinate limitation (Hooker). 2. To a degree indefinite (Ray).

INDEFINITUDE. s. (from indefinite.) Quantity not limited by our understanding, though yet finite (Hale).

INDELIBERATE. a. (in and delibeINDELIBERATED. rate.) Unpremeditated; done without consideration (Bramhall).

INDE LIBLE. a. (indelibilis, Latin.) 1. Not to be blotted out or effaced (Gay). 2. Not to be annulled (Sprat.)

INDE LICACY.s. (in and delicacy.) Want of delicacy; want of elegant decency (Add.). INDE/LICATE.a. (in and delicate.) Wanting decency; void of a quick sense of de

cency.

INDEMNIFICATION, s. (from indemnif.) 1. Security against loss or penalty. 2. Keimbursement of loss or penalty.

To INDEMNIFY. v. a. (in and demnify.) 1. To secure against loss or penalty. 2. To maintain unhurt (Watts).

INDEMNITY. s. (indemnité, Fr.) Security from punishment; exemption from punishment (K. Charles).

To INDE'NT. v. a. (in and dens, a tooth, Latin.) To mark any thing with inequality like a row of teeth; to cut in and out; to make to wave or undulate (Woodward).

To INDENT. v. n. (from the method of cut ting counterparts of a contract together.) To contract; to bargain; to make a compact (Decay of Piety).

INDENT. 8. (from the verb.) Inequality; incisure; indentation (Shak.).

INDENTATION.`s. (in and dens, Latin.) An indenture; waving in any figure (Woodward).

INDENTED, in heraldry, is when the outline of an ordinary is notched like the teeth of

a saw.

INDENTED LINE, in fortification, the same with what the French engineers call redent, being a trench and parapet running out and in, like the teeth of a saw; and is much used in irregular fortification.

INDENTURE, is a writing, containing a conveyance between two or more, indented or cut unevenly, or in and out, on the top or side, answerable to another writing that likewise comprehends the same words. Formerly when deeds were more concise than at present, it was usual to write both parts on the same piece of parchment, with some words or letters written between them, through which the parchment was cut, either in a straight or indented line, in such a manner as to leave half the word on one part and half on the other; and this custom is still preserved in making out the indentures of a fine. But at last, indenting only hath come into use, with out cutting through any letters at all, and it seems at present to serve for little other purpose, than to give name to the species of the deed: as an apprentice's indenture.

INDEPENDENCE. 8. (Independance, INDEPENDENCY.) Fr.) Freedom; exemption from reliance or control; state over which none has power (Addison).

INDEPENDENT. a. (independant, Fr.) 1. Not depending; not supported by any other; not relying on another; not con. trolled (South). 2. Not relating to any thing else, as to a superior cause or power (Bent.). INDEPENDENTS, a sect of protestants in England and Holland; so called, as deny ing not only any subordination among their clergy, but also all dependency on any other assembly.

They maintain that every separate church, or particular congregation, has in itself radically and essentially every thing necessary for its own government; that it has all ecclesias

tical power and jurisdiction; and is not at all subject to other churches, or their deputies, nor to their assemblies, or synods.

Robinson, the founder of the sect, makes express use of this term in explaining his doctrine relating to ecclesiastical government: Cœtum quemlibet particularum (says he, in his Apologia, cap. 5. p. 22.) esse totam, integram, et perfectam ecclesiam ex suis partibus constantem, immediate et independenter (quoad alias ecclesias) sub ipso Christo. It may probably have been from this very passage, that the title of independents was originally derived. The disciples of Robinson, originally called Brownists, because John Robinson, the founder of this sect, was pastor of a congregation of Brownists that had settled at Leyden, did not reject the appellation of Independents. It was certainly utterly unknown in England before the year 16-10; at least it is not once mentioned in the ecclesiastical canons and constitutions that were drawn up, during that year, in the synods or visitations held by the archbishops of Canterbury, York, and other prelates, in which canons all the various sects, that then subsisted in England, are particularly mentioned. See Wilkins's Concilia Magnæ Britanniæ et Hiberniæ, vol, iv. cap. 5. p. 548.

The first independent, or congregational church in England, was set up in the year 1616, by Mr. Jacob, who had adopted the religious sentiments of Robinson. The Independents, though sprung originally from a congregation of Brownists, were much more commendable than the latter, both in the moderation of their sentiments and the order of their discipline. The Brownists, or BARRowISTS, as we have already mentioned under that article, allowed all ranks and orders of men promiscuously to teach in public, and to perform the other pastoral functions; whereas the Independents had, and still have, a certain number of ministers, for the most part regularly educated, chosen respectively by the congregations where they are fixed; nor is any person among them permitted to speak in public, before he has submitted to a proper examination of his capacity and talents, and been approved of by the congregation to which he ministers. The charge alleged against them by our historian Rapin, (Hist. of England, vol. ii. p. 514, fol. ed.) who says, that they could not so much as endure ordinary ministers in the church, &c. is, therefore, evidently false and groundless. He was led into his mistake by confounding the Independents and Brownists. There are other charges, no less unjustifiable, that have been urged against the Independents, by this celebrated historian, and by others of less note. Rapin says, that, with regard to the state, they abhorred monarchy, and approved only a republican government. This might have been true with regard to several persons among the Independents, in common with